When Shirley M. Hufstedler became the nation's first secretary of education last week she took over the federal bureaucracy's equivalent of a National Football League expansion team -- mostly old faces, big hopes and glory first-year prospects.

It is not likely that the former California jurist will spend much of her time in lofty arguments over education philosophy. Instead, Hufstedler must wrestle with such problems as how to pull together a department now scattered at 11 locations around the city -- including six other existing Cabinet departments -- and how to circulate a memo to her top staff members in less than the three days it now takes.

And in a city that thrives on acronyms, it is not even clear what the new department should be called. "So far I've seen D-E, D-little o-E and D-little o-Ed," said a federal education official.

To add to her confusion, the education lobby if already deeply involved in the new department. "Education is the biggest business in Washington and everyone but the janitors is lining up trying to get a piece of the pie," a weary transition staff official said last week. "The last time we counted I think we had seen 18 different groups just involved in education for Indians."

The new secretary also will have to deal with a disgruntled Department of Health, Education and Welfare which stands to lose one-third of its territory to Hufstedler's department. According to some officials, HEW has already launched a vigorous rear guard fight.

For example, when federal transition officials sought to tap the HEW pool of several hundred auditors to oversee the Education Department's $6 billion higher education budget recently, they met a cool reception. HEW grudgingly offered the transition team only a dozen of its auditors.

Then there is the NASA problem. The National Aeronautics and Space Administration is firmly entrenched in its own headquarters on the top three floors of the new Education Department building. NASA officials have ignored past pleas from HEW, which had the building before, to move on. Some space officials have even hinted darkly of national security problems if they are booted out.

Senior NASA officials acknowledged this week that they have no particularly sensitive equipment lodged in the agency's offices in the building. But the location midway between the White House and the Capitol amid a cluster of federal offices -- is considered choice.

"We definitely do not want to move anywhere else," said a NASA official.

That leaves Hufstedler in the ultimate embarrassing position for a top federal bureaucrat. Her own office in her own building has a view that is inferior to the one from the office of her tenant, NASA Administrator Robert Frosch, three flights up.

Moreover, because of NASA's presence, the new Education Department headquarters will not carry any shiny nameplate for a while at least. Instead, it will remain plain old FOB 6.

"I always thought it sounded a little like we were working somewhere in the Kremlin," said former education commissioner Ernest Boyer. "I never did find out where FOB 1 through 5 were located."

Boyer and other federal officials predicted that the most serious problem facing space for all of its far-flung branches. Right now the department includes offices located at the departments of Labor, Agriculture, Defense, State, Justice and HEW.

"When I was there it was so scattered that every time I sent out a memo to my top people it took three days to reach everyone," said Boyer. "It was terrible for morale. We tried to send memos and Christmas cards just so they knew that we knew where they were."

In the end, in the view of some observers, Hufstedler may have her hands full just avoiding any new additions to the already legendary store of horror tales that surrounds the federal education bureaucracy.

The prospect that the 54-year-old former federal judge may be trapped for the next opening on the U.S. Supreme Court could make that job more difficult. But she described her enthusiasm for the new job in eager terms during her Senate confirmation hearing last month.

"Nothing gives me greater pleasure than to take a large pair of shears and cut through red tape," she told the members of the Senate Committee on Labor and Human resources. The senators beamed, but the audience packed with lobbyists and other members of the education establishment did not.

Hufstedler will have to work under tight budget limitations. About half of the new department's proposed first-year $14 billion budget already is locked by law into aid to higher education, most of it for student aid programs. The rest, for the most part, is divided between elementary and secondary school programs, which are also run under existing formulas set by law.

Her new department will include about 17,000 employes. About 11,000 of them will be personnel in overseas dependent schools but the rest are generally represented by a thicket of special interests, each one seemingly equipped with a watchful congressional sponsor.

At her confirmation hearing last month Hufstedler was not pressed on her views about education theory. Instead, the senators quickly made sure their pet interests such as museum services and libraries were well known to the new secretary.

Hufstedler will have to juggle those interests with a pledge by President Carter to cut 500 jobs from the education bureaucracy during its first 18 months. The entire department must be ready to go within six months, under federal requirements.

"The public has very little tolerance with long startups so we're going to have to hit the ground running," said Howard Messner, an official of the Office of Management and Budget assigned to help set up the new department.

Messner talks about his task with the brisk optimism of a man who already has helped construct the Department of Energy and the Environmental Protection Agency. It takes about five years to get everything going smoothly, he said.

But before that comes the bureaucratic minutiae such as whether an HEW employe qualifies to move to the new Education Department because of the hours spent on education subjects. And if he does, can he take desk with him?

"We go desk by desk," said Messner. "We fight over everything from power lines to swivel chairs."

And hard feelings arise occasionally. One group of HEW employes slated to be moved to the new department several months from now were dismayed to discover recently that their coveted parking permits were abruptly canceled when word of their departure leaked out.

Although Hufstedler and about 30 senior Education Department officials began moving into the department's new hadquarters last week, the bulk of the moves will not take place until officials acquire additional space nearby.

In the meantime, however, the wheels of the bureaucracy, once set in motion, continue to turn. About a dozen federal task forces will meet through next year to help get the new department going.

"Right now they are scattered all over the city," Messner said. "Our next job will be to consolidate the task forces."